Download Presentation

Number-Theoretic Algorithms

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

Presentation Transcript

1. Number-Theoretic Algorithms

2. Prime Number: 2, 3, 5, 7, 11, 13….
Composite number: 4, 6, 8,…..

3. Thm1: (Division Theorem)
For any integer a and any positive integer n, there are unique integers q and r such that 0?r<n and a=qn+r.
q=?a/n? is the quotient of the division.
r= a mod n is the remainder of the division.
a =?a/n?n+(a mod n)
Zn={0,1,2,…,n-1}

4. Greatest Common Divisor(GCD) Gcd(24,30)=6, gcd(5,7)=1
Thm2: If a and b are any integers, not both zero, then gcd(a,b) is the smallest positive element of the set {ax+by:x,y?Z} of linear combinations of a and b.